### The Regge bootstrap for weakly coupled dual model amplitudes

Dual models describe the tree-level exchange of infinitely many higher spin resonances, as in tree-level string theory and large N gauge theories. They are the simplest non-trivial scattering amplitudes that one can hope to build explicitly. Yet, numerically bootstrapping them has proven extremely difficult, in part because of the slow convergence of their expressions as infinite sums. In this talk I will present a numerical linear programming bootstrap to construct dual model amplitudes from the data of their Regge trajectories. The bootstrap method relies on an efficient parametrization of the amplitude in terms of Mandelstam-Regge poles, and a thorough understanding of the analytical structure of this expansion in the complex plane. After introducing some basic notions on Regge theory and explaining the method, I will show some first results obtained with it: Firstly I will explain how it is possible to "rediscover" the Veneziano amplitude within this framework by constraining our ansatz for the amplitude to a restricted parameter space, and then I will use the lessons learned from this exercise to investigate a toy-model deformation with bending trajectories mimicking some features of QCD.

**16 January 2024, 14:00**